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Subject Test Math 2

Question 27 of 28

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SAT Subject Test

C equals negative 1.02 F plus 93.63

The linear regression model above is based on an analysis of nutritional data from 14 varieties of cereal bars to relate the percent of calories from fat left parenthesis F right parenthesis to the percent of calories from carbohydrates left parenthesis C right parenthesis. Based on this model, which of the following statements must be true?

I. There is a positive correlation between C and F.
II. When 20 percent of calories are from fat, the predicted percent of calories from carbohydrates is approximately 73.
III. The slope indicates that as F increases by 1, C decreases by 1.02.

Select an Answer

II only

Correct Answer: 
No

I and II only

Correct Answer: 
No

I and III only

Correct Answer: 
No

II and III only

Correct Answer: 
Yes

I, II, and III

Correct Answer: 
No

The correct answer is D.

Statement I is false: Since C equals negative 1.02 F plus 93.63, high values of F are associated with low values of C comma which indicates that there is a negative correlation between C and F.

Statement II is true: When 20 percent of calories are from fat, F equals 20 and the predicted percent of calories from carbohydrates is C equals negative 1.02 left parenthesis 20 right parenthesis plus 93.63 almost equal to 73.

Statement III is true: Since the slope of the regression line is negative 1.02, as F increases by 1, C increases by negative 1.02 left parenthesis 1 right parenthesis equals negative 1.02; that is, C decreases by 1.02.

Question Difficulty: 
hard